General criteria of the strength of isotropic media

The limit surfaces of isotropic materials are considered in the invariant spaces of the stress tensor. The general requirements that must be met by limit surfaces are formulated. A three-invariant strength criterion for isotropic media sensitive and insensitive to hydrostatic pressure is given in general form. The convenience of analyzing strength criteria in the two-dimensional space of the base invariants of the stress tensor is demonstrated.Moscow. Translated from Mekhanika Polimerov, No. 2, pp. 251–261, March–April, 1971.     

Surface Bundles with Nonvanishing Signature

Using the theory of Lefschetz fibrations and recent advances in mapping class group theory, surface bundles over surfaces with nonzero signature and small base genus are constructed. In particular, a genus-5 fibration over the surface of genus 26 with nonzero signature is given –- improving former results on the possible base genera for surface bundles over surfaces with nonzero signature.     

Polymer fractography and fracture kinetics

The fractographic method makes it possible to determine the test temperature and time at which anomalies appear in the temperature-time dependence of the strength of polymethyl methacrylate and polycaprolactam by finding the conditions of disappearance of specular zones from the fracture surfaces of these polymers. For PMMA these values are –40°C and 10^–2 sec, for PCL –120°C and 10^–7 sec, respectively.For communication 1 see [2].Ioffe Physicotechnical Institute, Academy of Sciences of the USSR, Leningrad. Translated from Mekhanika Polimerov, No. 2, pp. 232–237, March–April, 1971.     

Constructing convex limit surfaces in material mechanics

In our previous paper [3], a method of constructing convex surfaces in 6D space of symmetric second-rank tensors by means of deforming the unit sphere S⁵ into a conoidal surface has been considered. Now we extend this method to parabolic surfaces and to the case where the shape of the surfaces depends also on the third tensor invariant. The resulting equations can be utilized for specifying the limit surfaces in the mechanics of isotropic and anisotropic solids. Some examples on approximating data on the experimental strength are presented.Institute of Polymer Mechanics, Latvian Academy of Sciences. Riga, LV-1006 Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 3, pp. 339–349, May–June, 1996.     

Generalized temperature-time characteristic of the strength and hardness of amorphous polymer materials

A new generalized characteristic of the strength and hardness of amorphous polymer materials is developed using two geometric surfaces, viz., of strength and stress relaxation. The combination of these surfaces determines the service range of the polymer material. For the polyarylate of isophthalic acid and phenolphthalein the service range is determined exclusively by the strength surface.Mekhanika Polimerov, Vol. 1, No. 4, pp. 89–91, 1965     

An alternative version of constructing limit surfaces for anisotropic solids

This paper deals with constructing closed everywhere smooth surfaces in 6D space of symmetric second-rank tensors by means of a conoidal anisotropic transformation of the unit sphere S⁵. A special case of such transformations is proposed and the surface convexity conditions are pointed out. These surfaces can be utilized in the strength and plasticity theories of isotropic and anisotropic solids.Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 4, pp. 488–493, July–August, 1995.     

Equilong-term strength surfaces of organic textolite in the plane stressed state

Conclusion Long-term strength tests of textolite were conducted for seven different particular cases of the plane stressed state. Maximum times to failure for which experimental data were obtained reach 2500 h. It is established from analysis of the test results that the experimental long-term strength curves for the types of stressed state under consideration are closely similar. The condition of long-term strength in the general case of the plane stressed state for constant levels of stresses is taken as the equation of the short-term strength surface in which the time factor is introduced parametrically; in this case, the apparent observance of similarity between equilong-term strength surfaces makes it possible to express the tensor components characterizing the long-term strength by tensor components of the short-term strength surface and a certain monotonically decreasing time function, which is independent of the form of stressed state.Translated from Mekhanika Kompozitnykh Materialov, No. 1, pp. 51–56, January–February, 1979.     

Investigation of the adhesion strength of carbamide resins

The adhesion of carbamide resin to clean or treated fiber glass surfaces has been determined. The effect of this adhesion on the strength of glass-reinforced plastics is examined.Moscow Mendeleev Chemical Engineering Institute. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1119–1121, November–December, 1968.     

Generalized thermoelastic waves in a layer with a boundary condition that is nonlinear with respect to temperature

A solution for the unsteady, generalized problem of thermoelasticity is constructed and investigated for a plane layer on one of whose surfaces there is given a generalized boundary condition of the third kind with a temperature-dependent heat-transfer coefficient.Translated from Matematicheskie Melody i Fiziko-mekhanicheskie Polya, No. 26, pp. 31–35, 1987.     

Strength of an organic/glass fiber-reinforced textolite in plane stress

Conclusions An analysis of the results of testing hybrid glass organic textolites, containing layers of glass and organic fabric reinforcement in various proportions, along characteristic simple short-time quasi-static loading paths served as a basis for determining a family of strength surfaces for plane stress in the plane of reinforcement. The strength of the five materials investigated is described by a second-order surface equation with allowance for the difference in compressive and tensile strengths. The dependence of the strength surface tensor components entering into the strength equation on the structure parameter representing the relative content of organic and glass fabric in the hybrid textolite is investigated and described. The results obtained can be used in practical calculations for determining the optimum ratio of organic to glass fabric in hybrid material with allowance for the specific requirements to be met by the strength properties of the material when used for structural purposes.Translated from Mekhanika Kompozitnykh Materialov, No. 6, pp. 1021–1026, November–December, 1979.     

Temperature dependence of the strength of a woven composite in a plane state of stress

Conclusions On the basis of an analysis of test results obtained by typical patterns of simple momentary quasistatic loading at various temperatures within the 20–150°C range, we have found a family of strength surfaces for a woven organic plastic material in a plane state of stress in the reinforcement plane. These experimentally found strength surfaces can be approximated by the equation of a second-degree surface. It has been established that the range of safe states of stress in the stress space narrows nonuniformly with rising temperature; namely, this narrowing is accompanied by a shift of the center and a reorientation of the axes of the strength ellipsoid. We have revealed and described the temperature dependence of the components of the strength surface tensors involved in the strength criterion. The data can be used for predicting the strength of a composite material under consideration when the latter is subject to simple quasistatic loading patterns in the three-dimensional (₁₁, ₂₂, ₁₂) stress space in the reinforcement plane within a given test range of temperatures.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 452–457, May–June, 1978.     

Boundary-integral formulation of dynamic nonstationary problems for an elastic space with a mathematical cut along a nonclosed Lyapunov surface

By satisfying the boundary conditions on the discontinuity surfaces using specially constructed integral representations of the solutions, we obtain a system of boundary integral equations for the functions of the opening of the cut.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 158–161.     

Comparative micromechanical analysis of nonelastic behavior of unidirectional plastics with tetragonal and hexagonal structures

A mathematical model for determining the effective elastic properties and describing the processes of inelastic deformation and damage accumulation of unidirectional fiber-reinforced composites with tetragonal and hexagonal structures is developed. A comparative analysis of the effective elastic moduli of glass, boron, organic, and carbon unidirectional plastics shows that, if the fiber volume fraction does not exceed 0.5, the effective elastic properties calculated by the models presented give closely related results. The calculation results for nonlinear fields of deformation and failure are presented and the limiting strength surfaces of fibrous glass plastics with hexagonal and tetragonal structures are obtained for different transverse loading paths. It is found that the structure of a composite affects significantly its strength properties.Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000).Perm' State Technical University, Perm', Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 4, pp. 455–464, July–August, 2000.     

Static fatigue of glass-reinforced plastics

Nonlinear damage accumulation rules are usually constructed on the basis of certain hypotheses derived from semiempirical considerations. A method is proposed for constructing an averaged nonlinear damage accumulation rule based on the direct utilization of the results of static fatigue tests on glass-reinforced plastic specimens. Numerical examples of the calculation of the static fatigue strength under repeat loading with a given strength criterion are presented.Sverdlovsk Branch of the Steklov Mathematical Institute, Academy of Sciences of the USSR. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 492–497, May–June, 1969.     

Experimental investigation of the anisotropy of strength of bolted joints of laminated composites upon variation of geometric and design parameters

Conclusion In the present work we investigated the anisotropy of the characteristics of tensile (buckling) strength and elasticity of plates made of KMU-4L in a bolted joint in a wide range of parameters of the material (stacking, number of layers), geometric parameters of the joint, parameters of the fastening element and of design parameters. An analysis of the results showed that the strength of the bolted joint under static loading can be increased for thin plates with h = 1–2 mm by local reinforcement of the zone of the hole by layers with = ±45 °, and also by increasing the moment of preliminary tightening; for plates with h = 3–4 mm the only feasible measure is increasing the moment of preliminary tightening to 20–40 Nm. All the results of the experiment were graphically generalized in the form of surfaces of maximal stress; this made it possible to predict the load bearing capacity of a joint for intermediate values of the parameters by calculating the safety factors.Translated from Mekhanika Kompozitnykh Materialov, No. 2, pp. 268–272, March–April, 1990.     

Temperature-time dependence of strength of organic fibers based on p-polyamides

Conclusions An experimental investigation of the temperature-time dependence of the strength of organic fibers based on p-polyamides has been performed. The possibility has been established of using the temperature-time analogy method to predict the lifetime of fibers from the results of rapid tests at elevated temperatures. A generalized curve of long-term strength has been constructed, and the coefficient of temperature shear has been determined. An approximation of the experimental long-term strength data has been carried out by a formula which satisfies the temperature-time analogy principle.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 470–473, May–June, 1978.     

The Effect of Surface Treatment of F-12 Aramid Fibers with Rare Earths on the Interlaminar Shear Strength of Aramid/Epoxy Composites

Solutions of a rare-earth modifier (RES) and the epoxy chloropropane (ECP) grafting modification method are used for the surface treatment of F-12 aramid fibers. The effects of RES concentration on the interlaminar shear strength (ILSS) of F-12 aramid fiber/epoxy composites are investigated in detail, and the fracture surfaces of ILSS specimens are analyzed by SEM. It is shown that the RES surface treatment is superior to the ECP grafting treatment in promoting the interfacial adhesion between aramid fibers and the epoxy matrix. However, the tensile strength of single fibers is almost unaffected by the RES treatment. The optimum ILSS is obtained at a 0.5 wt.% content of rare-earth elements.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 2, pp. 265–272, March–April, 2005.     

“Fundamental” and “practical” adhesion in polymer-fiber systems

The relationship between adhesion and bond strength in thin fiber-polymer matrix systems was studied. Adhesive interaction in composite materials was analyzed within the scope of thermodynamic and molecular-kinetic theories of adhesion. Methods based on wetting are shown to give poor estimation of the work of adhesion in fiber-polymer systems, which is due to their low sensibility to donor-acceptor interactions taking place at the interface. Important information about the acidity and basicity of contacting surfaces can be obtained by using inverse gas chromatography to investigate the thermodynamics of adsorption. The calculation of the work of adhesion including acid-base interactions shows the best agreement with the bond strength in the same systems. The local (ultimate) interfacial shear strength is proposed to characterize the quality of fiber-matrix bonding. Analysis of the relationship between the work of adhesion and adhesive pressure for various systems allowed us to differentiate the dispersive and acid-base components of the local bond strength as well as to estimate distances characteristic of these twoTypes of interaction. For dispersive forces, our estimation gives 7–8Å, i.e., of an order of magnitude of the center-to-center distance for van der Waals interactions. At the same time, the acid-baseInteractions have a characteristic range of 4–5Å and can be attributed to hydrogen bonding. The agreement between the calculated distances and literature data is evidence for the applicability of the proposed method to the analysis of the adhesive interaction in fibrous polymer composites.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 4, pp. 431–446, July–August, 1998.     

Concentration of electroelastic fields in a composite piezoceramic plate with defects crossing the interface

The characteristics of fracture and strength of a composite piezoceramic plate with defects in the form of cracks and holes situated in both of the plate components are investigated. The corresponding boundary-value problems of electroelasticity are reduced to systems of singular integral equations by constructing integral representations of the complex potentials. The results of numerical realization of the constructed algorithms are reported.Presented at the 10th International Conference on the Mechanics of Composite Materials (Riga, April 20–23, 1998).Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 6, pp. 777–786, November–December, 1998.     

Geometry of theories of strength

The author proposes a geometrical method of describing limit states by means of surfaces in stress, strain or stress-strain space using surface tensors. The history of the geometrical representation of theories of strength is briefly surveyed.Mekhanika Polimerov, Vol. 2, No. 4, pp. 519–534, 1966